The present invention relates generally to a mathematical teaching device, and more specifically to a device that teaches various mathematical functions related to fractions.
One embodiment of the device includes a base sheet to which is attached pivotally a ruler. The base sheet is labeled with various fractions, distributed in a hierarchical relationship about the sheet. Each fraction includes a numerator, a denominator and a dividing line separating the numerator from the denominator. The dividing line of each fraction is sloped to represent a mathematical relationship of the numerator to the denominator. For example, the fraction bar may represent graphically the slope of a hypotenuse of a right triangle having a vertical side the length of the numerator, and a horizontal side the length of the denominator.
The base sheet also may be labeled with lines in a grid, the lines crossing to define grid points. The spacing of the lines in the grid may be equidistant, and the crossing of the lines may be perpendicular so that the lines define a series of squares. Alternatively, a first set of lines may be spaced at a first interval, and a second set of lines generally perpendicular and overlapping the first set may be spaced at a second interval, so that the first and second sets of lines collectively define rectangles, but not squares. As a further alternative, the lines defining the grid may be parallel, but the first and second sets need not be perpendicular to each other, so that the lines define a series of parallelograms, that may, but need not be, equilateral.
Preferably, the ruler is attached to the base sheet at a grid crossing, and this attachment defines an origin for the grid. Furthermore, the grid lines define squares, and the ruler is labeled in increments conforming to the unit length of the sides of the squares, along a reference line extending approximately from the grid origin. The ruler is rotatable about the origin, and is clear so that the relationship of the labeling on the ruler to the labeling on the grid may be observed readily. Each fraction is located at a grid point, and the fraction bar for each fraction is oriented to extend along a line from the corresponding grid point to the grid origin. The ruler includes an indicator line extending directly away from the grid origin, so that the indicator line of the ruler closely overlaps the fraction bar for a fraction at a slope approximately equal to the slope of the fraction bar, when the indicator line is aligned with the grid point for the fraction.
Yet other embodiments are envisioned within the scope of the present invention. For example, the ruler could be manufactured with a slot or other external geometry that would allow a marking pen to trace a line along the centerline of the ruler. This could be used in combination with erasable pens, or with a removable, clear, intervening sheet that could be placed between the ruler and the base sheet, so that various tracings and notations could be made by either the teacher or a student. In those embodiments in which the intervening sheet is removable, various tracings could be made for various problems, and the solutions shown on the intervening sheets could be compared by the student and teacher.
In the preferred embodiment, there are 11 vertical lines and 11 horizontal lines defining the grid. The last vertical line further is labeled with the decimal and percentage equivalent of the fractions listed along the line. Alternative quantities of lines could be used to demonstrate use of the device for other base counting systems such as base 8 or base 16.
It is an object of the present invention to explore the interrelationship between various mathematical concepts.
Additional objects and advantages of the present invention will be understood more readily after a consideration of the drawings and the Description of the Operations.